1. Field of the Invention
The present invention relates to a light scanning system that is provided with an anamorphic convex lens, such as a cylindrical lens for the purpose of optically correcting errors in the inclination of the reflecting surfaces of a light deflecting device, such as a polygon mirror, or for the purpose of shaping the light beam emitted from a light source. The present invention further relates to a light scanning system provided with a tapered polygon mirror having a plurality of reflecting surfaces that are inclined by substantially the same angle with respect to the axis of rotation.
2. Description of the Prior Art
An example of a light scanning system already in use is shown in Japanese patent publication No. 144517/1982.
In the case of such a light scanning system, a light beam emitted from a light source is reflected by a polygon mirror and is converged onto a subject to be scanned through a single lens having a toric surface, forming a spot of light on the subject. The spot scans the subject as the polygon mirror is rotated.
In some types of light scanning systems, a cylindrical lens is placed in an optical path between the light source and the polygon mirror. The cylindrical lens functions to shape the beam of light emitted from the light source or to reduce the effects of errors in the inclination of the reflecting surfaces of the polygon mirror used as a deflecting device. Further, such cylindrical lens and the above-mentioned single lens constitute in combination an anamorphic optical system. In this specification, the phrase "error in the inclination of a reflecting surface" means the inclination angle of the reflecting surfaces with respect to the axis of rotation arising from some cause concerned with the manufacturing process, the reflecting surface having to be parallel with the axis of rotation.
In the case of the above-mentioned anamorphic optical system, one of two principal meridians (generatrix, in the case of a cylindrical lens) of each optical element must substantially coincide with the principal scanning direction. The phrase "principal meridians" means the intersections of the lens surface and the principal sections including the optical axis where the power of the lens has a maximum or minimum value. The optical elements for use in the light scanning systems under consideration are designed to have two principal meridians which intersect each other at right angles. Further, the phrase "principal scanning direction" means the direction in which the spot of light scans, a direction within a plane which is perpendicular to the axis of rotation of the polygon mirror. The phrase "secondary scanning directions," to be described below, means the directions perpendicular to the principal scanning direction.
The directions of the above-defined principal meridians may sometimes be erroneous due to processing errors or assembling errors of the element, and such erroneously directed principal meridians will deteriorate the converging characteristics and spot configurations on the subject surface to be scanned. Such deterioration is greater at the peripheral regions than at the center of the subject to be scanned.
If each optical element is processed to a high accuracy so as to more accurately coordinate the principal meridians with the principal scanning direction, the mass production efficiency becomes lower. Besides, the convex lens placed in the optical path between the light source and the deflecting device, which is employed so as to compensate for inclination errors and shape the light beam, is generally small in size. Hence, it is difficult to accurately process such a small element. Moreover, accurately assembling processed optical elements in a system should be performed within small tolerances.
Meanwhile, the above-mentioned polygon mirror is produced by a process that includes the steps of shaping a material such as glass or aluminium alloy, into a predetermined prismatic form, polishing the side surfaces to form reflecting surfaces of a predetermined accuracy, and plating the side faces with silver or aluminium.
There is, however, a problem in that it is difficult (and, hence, it takes a long time) to perform the step of polishing the sides of the prism up to the required accuracy. The step must be repeated for each one of the products. Thus, the mass production efficiency is poor and the manufacturing cost is high.
Recently, a polygon mirror has been proposed which can be produced as a single body by injection molding of plastics using a mold. To produce polygon plastic mirrors, only a mold is required but high-accuracy processing of each product is not required, so that a high mass production efficiency can be achieved.
To produce plastic polygon mirrors of having reflecting surfaces parallel to the axis of rotation, a split mold with a slide core must be used, since any draft cannot be imparted to the reflecting surfaces. To produce a split mold, many steps must be performed, raising the cost. In addition, it is difficult to achieve high accuracies.
Where drafts can be imparted to the reflecting surfaces, a mold of high accuracy can be produced. It is possible to reduce the deterioration of the accuracy due to abrasion of the mold, and the performance of the products will become higher. If, however, a tapered polygon mirror is incorporated into a light scanning system, two problems occur, as described below.
The first problem lies in that the scanning line on the subject to be scanned will be inclined or curved so that a formed pattern will be distorted.
This problem can be solved using means for compensating for errors in the inclination of reflecting surfaces which has already been in use. Examples of such means are disclosed in Japanese laid-open patent application Nos. 144517/1982 and 245129/1986. In the former, a line image is formed on the reflecting surface. The latter includes a scanning lens which has a shorther focal length in the secondary scanning direction than in the principal scanning direction so as to reduce the effect of inclination errors, and in which the refracting power in the secondary scanning direction can be compensated for by means of a convex cylindrical lens that is placed before the deflecting device.
It is known that the scanning line can be corrected by making the scanning lens eccentric in the above-mentioned compensation is insufficient.
The second problem lies in that, where a convex cylindrical lens and an anamorphic f.theta. lens are placed before and after a polygon mirror, torsion will apparently occur between the generatrix of the convex cylindrical lens and the principal meridians of the f.theta. lens due to the torsion of the light beam occurring upon reflection. The quality of the imaging function is thus lowered.
The reason for the occurrence of the second problem will be explained with reference to FIGS. 13-15.
In the case of FIG. 13, reflecting surfaces R are parallel to an axis of rotation l, and therefore there are no inclination errors. An axis x in this figure represents the optical axis of an f.theta. lens, not shown, and dashed line H represents a normal to the reflecting surface R. .theta. represents the scanning angle formed by optical axis L.sub.2 of a reflected light beam and an x-axis; p represents a polygon normal angle formed by normal H and the x-axis; w represents an incident angle formed by optical axis L.sub.1 and the x-axis. If there is no taper, the scanning angle .theta. is expressed as follows: EQU .theta.=2p-w,
and the angle formed by the optical axis L.sub.2 of the reflected light beam and a plane (plane of the sheet of the drawing) containing the principal scanning direction is 0.degree..
When the reflecting surfaces R are imparted a small tapering angle .delta. (see FIG. 14) and the remaining elements are the same as the foregoing, the scanning angle .THETA. is substantially the same as that described above and can be expressed by: EQU .theta.=2p-w.
With respect to FIG. 15, it is assumed that the x-axis represents the optical axis of an f.theta. lens (not shown), a y-axis represents the scanning direction, a z-axis represents a direction parallel to the axis of rotation l, and that the dashed line H represents a normal to the reflecting surface R. Angle .alpha. formed by the optical axis of the reflected light beam and the principal scanning plane (i.e. x-y plane) is expressed by the following equation: EQU .alpha.=sin.sup.-1 (sin 2.delta..multidot.cos(p-w)).
When the value of .delta. is small, EQU .alpha.=2.delta..multidot.cos(p-w).
Torsion angle .beta. of the light beam due to reflection may be expressed by the following equation: ##EQU1## When the value of .delta. is small, ##EQU2##
The torsion of the light beam will cause an apparent inclination between the generatrix of the convex cylindrical lens and the principal meridians of the f.theta. lens which is in the principal scanning plane, and as a result the wave front aberration becomes worse.